Emory is mounting 3 shelves of 12 3/4 in apart on a wall. If each board is 3/4 in. thick, what is the total vertical space occupied by the set of shelves?
3 * (3/4) = 9/4 = 2 1/4
2 * 12 3/4) = 24 6/4 = 25 2/4
24 2/4 + 2 1/4 = 26 3/4 inches
Ooops -- typo!
25 2/4 + 2 1/4 = 27 3/4 inches
thank you miss sue
You're welcome, Lori.
To find the total vertical space occupied by the set of shelves, we need to calculate the combined height of the shelves and the gaps between them.
First, let's calculate the height of one shelf. We know that each board (shelf) is 3/4 inch thick. So, the height of one shelf is 12 3/4 inches minus 3/4 inch (thickness of one board) which equals 12 inches.
Next, we need to calculate the combined height of the shelves. Since Emory is mounting 3 shelves, we multiply the height of one shelf (12 inches) by the number of shelves which gives us: 12 inches x 3 shelves = 36 inches.
However, we also need to account for the gaps between the shelves. Since there are only 2 gaps between the shelves, we need to subtract their combined height from the total. The combined height of the gaps is (2 x 3/4 inch) = 1 1/2 inches.
Finally, we subtract the combined height of the gaps (1 1/2 inches) from the total height of the shelves (36 inches) to find the total vertical space occupied by the set of shelves.
36 inches - 1 1/2 inches = 34 1/2 inches.
Therefore, the total vertical space occupied by the set of shelves is 34 1/2 inches.